Question

Two identical waves interfere at a point in the same medium having amplitudes $3\text{cm}$ and $5\text{cm}$. Which of the resultant amplitude is not possible?

• A. $2\text{cm}$
• B. $5\text{cm}$
• C. $6\text{cm}$
• D. $9\text{cm}$

Answer 1

The correct option is D $9\text{cm}$

The resultant amplitude,

$A_{\text{net}}=\sqrt{A_1^2+A_2^2+2A_1{A}_2\cos \varphi }$

For maximum amplitude, $\cos \varphi =1\Rightarrow A_{\text{net}}=|A_1+A_2|=|5+3|=8\text{cm}$

For minimum amplitude, $\cos \varphi =-1\Rightarrow A_{\text{net}}=|A_1-A_2|=|5-3|=2\text{cm}$

Therefore, the net amplitude lies between $2\text{cm}$ and $8\text{cm}$.

Hence, option $\left(D\right)$ is the correct answer.